Timeline for The direction that gets me closest to a given point in $\mathbb{R}^n$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 13, 2021 at 18:08 | comment | added | Yaakov Baruch | ERRATA. The last implication is wrong... monotonicity is true but what follows is the converse of what I stated: $\alpha\ge \beta/n\implies \sin(\alpha)\ge \sin(\beta)/n$ | |
| Mar 4, 2021 at 23:20 | comment | added | Lostsoul | In the light of your counter-example, I should re-consider my separation condition indeed. Many thanks for this. I had not realised that my condition is weaker so that the angle with the span of the other (n-1) vectors may not necessarily be greater than $\theta$. | |
| Mar 4, 2021 at 23:06 | comment | added | Yaakov Baruch | if the approximation $\frac{\sqrt{1+h^2 n-h^2}}{n}\ge\frac{1}{n}$ seems too rough for large $\theta$'s, one can express $h^2$ in terms of $n$ and $\tan(\theta)$, and end up with the exact formula $\sin(\frac{\pi}{2}-\alpha)=\sin(\theta)\sqrt{\frac{(n-1)\tan(\theta)^2+n}{n((n-1)\tan(\theta)^2+n^2)}}$. | |
| Mar 4, 2021 at 17:41 | history | edited | Yaakov Baruch | CC BY-SA 4.0 |
deleted 1 character in body
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| Mar 4, 2021 at 17:28 | history | edited | Yaakov Baruch | CC BY-SA 4.0 |
edited body
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| Mar 4, 2021 at 17:22 | history | edited | Yaakov Baruch | CC BY-SA 4.0 |
improved readability
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| Mar 4, 2021 at 17:14 | history | answered | Yaakov Baruch | CC BY-SA 4.0 |